Given, x2+3|x|+2=0 |x|:x<0→−,x>0→+ For x<0 x2+3(−x)+2=0 x2−3x+2=0 (x−1)(x−2)=0 x=1,2 But for condition, x<0,x=1,2 does not satisfy. For x>0 x2+3(x)+2=0 x2+3x+2=0 (x+1)(x+2)=0 x=−1,−2 But for condition, x>0,x=−1,−2 does not satisfy. Therefore there are no real roots